Length Definition and 1000 Threads

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre.
Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in.
Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object.Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).

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  1. The Baron

    What Happens to the Wavelength of Light as it Passes Through Water?

    I have a question, say a wave of light is emitted, and it passes through water, changing it's wave length to 380nm inside the water, once it comes out of the water, to vacuum will the wavelength remain at 380nm or will it change?
  2. F

    Relativity of Length: Understanding Length Contraction & Time Dilation

    a) We use the definition of speed: v = delta_L/delta_t delta_t = delta_L/v = 45000 m/(0.99540*3*10^8 m/s) = 1.55*10^-4 s b) We use the length contraction equation: delta_L = L_0*sqrt(1-v^2/c^2) L_0 = delta_L/sqrt(1-v^2/c^2) = 45000 m/sqrt(1-0.99540^2) = 469698 m However, the solution shows...
  3. O

    I Compute Length Contraction: Is ##l=1## a Possible Model?

    Sorry, I accidentally posted this while typing it up, then when I finished typing it I found the mistake that made me come here to make this thread. I'll still write it up just to make the thread somewhat useful, and then ask my follow-up question at the end I'm picking units so the speed of...
  4. B

    I How to calculate the focal length and focal point of collimator?

    I wanted to calculate the focal length and focal point of the collimator. The collimator diameter is 3mm, and I wanted to focus on the 100-micrometre active area of the detector.
  5. R

    I Length contraction and time dilation

    A long time ago, I was very impressed by a lecture on elementary special relativity which showed in simple math how the correct conclusion to the null results of the Michelson-Morley experiment were obtained by concluding a constant c but then adding a length contraction and time dilation. I...
  6. M

    MHB Uniform convergence - Length of graph

    Hey! :giggle: We define the sequence of functions $f_n:[0,1]\rightarrow \mathbb{R}$ by $$f_{n+1}(x)=\begin{cases}0 & \text{ if } x\in \left[ 0, \frac{1}{2n+3}\right ]\\ |2(n+1)x-1| & \text{ if } x\in \left [\frac{1}{2n+3}, \frac{1}{2n+1}\right ] \\ f_n(x) & \text{ if } x\in \left...
  7. MisterH

    A Fitness function for window length of filter

    Fitness function for window length of filter On a sinusoidal signal with amplitude 1, and period P, an exponential moving average (EMA) (with alpha = 1/n), and a linear weighted moving average (LWMA) (with window length n) are calculated; when you subtract the EMA from the LWMA, it can be seen...
  8. Kaguro

    Deriving length contraction using spacetime

    Deriving time dilation was easy: Imagine two events in frame O' at the same location. ##ds^2 = -c^2 dt'^2## The same viewed in O frame is: ##ds^2 = dx^2+dy^2 + dz^2 - c^2 dt^2## ##\Rightarrow dx^2+dy^2 + dz^2 - c^2 dt^2 = -c^2 dt'^2## ##\Rightarrow (\frac{dx}{dt})^2+(\frac{dy}{dt})^2+...
  9. Another

    Show the number of arrangements that give an overall length of L = 2md

    I know ## L = 2md = (N_+ - N_-)d ## then ## 2m = N_+ - N_- ## So I can write ##N_+## and ##N_-## in term N and m I don't understand the factor 2 multiplying in front of N!/[(N_+)!(N_-)!] How does multiplication by the number "2" give a physical meaning?
  10. D.S.Beyer

    B SR vs GR - Visual Difference between Length Contraction

    The 2 Bowling Balls Ball(a) & Ball(b) (a) is in acceleration of 10m/s^2 (b) is in at fixed position in a gravitational field where g=10m/s^2 In both cases the observer is: - perpendicular to the vector of acceleration - distant enough to be in empty flat space Question : In an instantaneous...
  11. cianfa72

    I The spacetime length of finite spacelike intervals

    Hello, I'm aware of the following topic has already been discussed here on PF, nevertheless I would like to go deep into the concept of "finite spacelike interval" in the context of SR and GR. All us know the physical meaning of timelike paths: basically they are paths followed through...
  12. P

    Chemistry Need Help with Bond Length Calculations of Acetylene

    Hey! I am trying to determine the bond length of acetylene by analysing the vibrational spectrum of both H-Acetylene and D-Acetylene. I was able to calculate both the rotational constant and the moment of inertia but am stuck now as to how I get to the correct solution. On the left is the...
  13. S

    How to find the length when trying to determine the shear

    The sketch that goes with the problem. My attempt at solving the problem: a) to get σ (I think this is called tension in english) we need the force,and we need the area.From the sketch we can see that the area is A = 6*2 and we convert those in m and than set in the formula we should get $$ σ...
  14. R

    Determining optimal barrel length for a projectile

    Hello, I was wondering of anybody has a formula to determine the optimal barrel length for a firearm using a particular cartridge? For example, the M855 cartridge which has a 62gr. projectile and uses WC-844 propellant, which has a known burn rate etc. The longer the barrel, the more...
  15. VictorMedvil

    B Is The Planck Length the smallest length possible?

    So, I was wondering is the Planck length the smallest length possible for measurement in physics? Please give as much details as to why or why not.
  16. I

    Minimum length x for no slipping

    I'm letting the weight of the hanger be W. Since there is no slipping, the total frictional force will be = total weight. When the load of 50W is placed at X, there'll be a normal force at the left end of the pole on top to the left, and another normal force at the right end of the pole at the...
  17. S

    How to find the focal length of a lens (Problem with a task)

    Hello. I need formulas for the focal length of a lens when I have refractive indices of two centers and two radii of curvature of spherical surfaces or one radius of curvature of spherical surfaces. I search the internet but can't find it.
  18. chwala

    Find the length XY from the rectangular diagram

    i saw this question on the internet. The people responding were of the opinion that the length##xy=1##, but no working...first of all is the answer ##1## correct? i am trying to find the steps to solution, i have managed to find an angle ##57.27^0## by cosine rule, i tend to think that i need...
  19. Athenian

    [Special Relativity] - Finding the Proper Length at Rest in Frame S'

    Currently, the only part of the textbook question that is completely throwing me off is "an angle of ##l=\sqrt{2}c##". If I am not mistaken, how am I suppose to interpret that as an angle and calculate for the answers of (a) and (b) accordingly? As for my attempted solution process of this...
  20. M

    I What is the purpose of the Prandtl Mixing Length for turbulent flow?

    Hi, I was recently learning about turbulent boundary layers and came across the 'Prandtl mixing length'. I am struggling to understand what the concept is and what its purpose is. I would appreciate any help or guidance of where I can look to gain a better understanding. The information I...
  21. S

    B What is the Length of a Compound Microscope?

    If we say "length of microscope", which distance does it refer to? Is it: a) the tube length (L), which is the distance between the focal point of objective and focal point of eye piece lens OR b) the distance (d) between objective and eye piece lens Thanks
  22. J

    Simple Wavelength Problem (wire of fixed length vibrating)

    When the question says 8 antinodes, doesn't that mean N=8? but when I do 2L/8, I get 0.24. To get the right answer you do 2LN, but that doesn't make sense to me for I thought the equation was 2L/N??
  23. P

    I 100 boxes of Length L, an application of the famous Particle in A Box

    Suppose I have 100 identical boxes of length L and the coordinates are x=0 at one end of the box and x=L at the other end, for each of them. Each has a particle of mass m. V=0 in [0,L], while it's equal to infinity in the rest of the regions. If I make a measurement on position of the particle...
  24. bq1892

    Describe the length of an electron's journey in its own frame of reference

    Lv = Lo / γ 1/γ =√(1-v^2/c^2) = √(1-0.8^2) = 0.6 Therefore Lv = Lo x 0.6 = 150 x 0.6 = 90m Therefore electron travels 90m in its own frame of reference (answer key solution) However, shouldn't the electron be assigned rest length, Lo, as its frame of reference is at rest with itself instead...
  25. S

    I To measure a Planck length would require a black-hole photon?

    I was viewing this video in which the narrator says that the energy of a photon that could discern a Planck length would require a photon of such high energy that it would be a de factor black hole. Is this accurate?
  26. lola1227

    Beats and Resonance - How to Find the Length With only Frequency?

    So, my thinking was that we use the formula V=f(lambda) and substitute the f so, V = 440(lambda) but then i don't have another number to cancel or rearrange by. And since closed air columns have the fractions of 1/4, 3/4, and 1 1/4 (5/4), we could divide by those?
  27. T

    How the flow angle along the blade would change along the length

    I am not sure how to do this at all or what exactly he is asking me. [Mentor Note -- Two threads on the same problem have been merged into one]
  28. sahilmm15

    B Length is the measure of intervals in space?

    What does 'intervals' mean here?
  29. A

    Conical Pendulum with varying string length

    Consider a conical pendulum like that shown in the figure. A ball of mass, m, attached to a string of length, L, is rotating in a circle of radius, r, with angular velocity, ω. The faster we spin the ball (i.e., the greater the ω), the greater the angle, θ, will be, and thus, the smaller the...
  30. J

    B Experimental Confirmation Length Contraction Velocity Addition

    What if any is the experimental confirmation for length contraction and the velocity addition formula?
  31. B

    A Levi-Civita Connection & Length of Curves in GR

    I am studying GR and I have these two following unresolved questions up until now: The first one concerns the Levi-Civita connection. There are two conditions which determine the affine connections. The first one is that the connection is torsion-free (which is true for space-time and comes...
  32. Monoxdifly

    MHB What is the Minimum Length of AP + PB?

    The point A is located on the coordinate (0, 5) and B is located on (10, 0). Point P(x, 0) is located on the line segment OB with O(0, 0). The coordinate of P so that the length AP + PB minimum is ... A. (3, 0) B. (3 1/4, 0) C. (3 3/4, 0) D. (4 1/2, 0) E. (5, 0) What I did: f(x) = AP + PB...
  33. V

    MHB Minimum Length of Longest Side in Inscribed Triangle

    In triangle ABC, ∠C = 90 degrees, ∠A = 30 degrees and BC = 1. Find the minimum length of the longest side of a triangle inscribed in triangle ABC (that is, one such that each side of ABC contains a different vertex of the triangle).
  34. cestlavie

    Length of sides of a wire loop in a uniform magnetic field

    If ##\tau= 0.0727, N=60, i=1.3, B=1.0,## and ##\theta=15##, I tried the following calculation: ##\tau=NIABsin\theta## ##\tau=NIs^2Bsin\theta## ##s^2=\frac {\tau} {NIBsin\theta}=\frac {.0727} {60*1.3*1*sin(15)}=0.0632 m=6.32 cm## The answer is probably right in front of me, but I don't know what...
  35. E

    How do you calculate the Kuhn length of a polymer?

    My lecturer said that as a first approximation, we can take the polymer chain to consist of ##n## freely jointed rods of length ##l##. That's just going to give$$\langle \vec{R}_n^2 \rangle = \langle \sum_{i=1}^n \vec{r}_i \cdot \sum_{j=1}^n \vec{r}_j \rangle = \langle \sum_{i=1}^n \sum_{j=1}^n...
  36. A

    Determining the minimum velocity when given height and length

    Now I've tried looking at the problem like this. Considering that a is the length off the vehicles that he is trying to jump over I would consider that to be s. The plane from which he starts (b) should be the h. So considering that he is jumping from a horizontal plane, gravity should also...
  37. U

    I Length Contraction & Time Dilation: Proving It

    I have been able to prove to myself that, based on Einstein's two postulates and the the Pythagorean theorem, that time dilates. From here how do I prove that length contracts? (All of this observing a frame that is moving relative to the proper frame at uniform velocity.)
  38. T

    B On time dilation and length contraction

    Hello there.About time dilation, could we provide a derivative of time in relation to one of the coordinates of the manifold we have taking time as a function and get something as a result?Or its integral?And about time dilation we have the formula that gives it between two clocks and an...
  39. R

    B LIGO Arm Length & Sensitivity: What's the Relation?

    [Moderator's note: Spun off from previous thread due to new question.] I have read here: http://backreaction.blogspot.com/2016/02/everything-you-need-to-know-about.html?m=1 That there is a proportionality between the size of LIGO arms and the wavelength of gravitational waves that it can...
  40. K

    Velocity, barrel length and bore volume

    Hello. How does a bullet propell inside a bore? What determine its velocity? I read that a bullet in cal .44 propelled by black powder from a 3” barrel is as powerful as a .25 ACP, however with a longer barrel, the velocity increase significant. With a 8” barrel a .44 black powder bullet is as...
  41. AN630078

    Trigonometry: finding an angle, area and length of sector of a circle

    1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...
  42. S

    B Light Clock & Length Contraction in GR

    Hi, can i use a light clock made out of mirrors a distance appart to measure whether there is length contraction in different regions of spacetime? If the clock speeds up then the distance between the mirrors decreased. If the clock slows down the distance between mirrors increased.
  43. X

    B Time Dilation & Length Contraction: Physics Explained

    So basically i know almost nothing about physics but i have this one curiosity and i hope you can help me ahah. For what i understand if you could move at the speed of light time would stop for you and you would see the whole universe age in a blink of an eye. But what if you could stand...
  44. S

    Uncertainty in the measurement of the focal length in this experiment

    ##\frac{1}{f}=\frac{1}{u}+\frac{1}{v}## ##f = \frac{u.v}{u+v}## Let: u + v = w → w = 250 mm ± 8 mm Percentage uncertainy of v = (3/50) . 100% = 6% Percentage uncertainty of u = (5/200) . 100%=2.5% Percentage uncertainty of w = (8/250) . 100% = 3.2% Percentage uncertainty of f = 6 % + 2.5 %...
  45. M

    Length of a Wave Train in Special Relativity

    I am confused about how to find the length of a wave train emitted within a time interval T and that is moving with speed c relative to a moving frame that is itself moving with velocity v. Apparently the answer is that the wave train's length is cT - vT, but I tried to plug in variables into...
  46. asmmanikanda

    MHB How to find a length of line in quadrilateral?

    AB and DC not parallel line., AB=55,BC=65,DC=76,DA=48 Ax=28,xD=20,By=37,yC=28 How to find length of xy?
  47. anemone

    MHB Find length that minimizes the perimeter

    Let $ABC$ be an equilateral triangle and let $D,\,E$ and $F$ be the points on the sides $AB,\,BC$ and $AC$ respectively such that $AD=2,\,AF=1$ and $FC=3$. If the triangle $DEF$ has minimum possible perimeter, find $AE$.
  48. T

    Multivariable Arc Length Problem: Weird Form with Parameterization

    Problem: See Attachment. Parts (a) & (b) are clear, but my confusion arises in (c)-- I feel like there is a much simpler form. While technically my answer is correct, there must be something I'm missing. I parameterized the curve C=(t, e^2t, e^2t) and got c'(t)=(1,2e^2t,2e^2t), which should...
  49. Stephen Bulking

    Length contraction and Time dilation for LIGHT?

    Radio wave travels at the speed of light 3x10^8 (m/s) Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years The answer is B But wouldn't the time in light's frame of reference be 0 and it's...
  50. E

    Limit of this expression for apparent length

    The apparent length of a rod is determined to be$$\tilde{L}(x_0) = \gamma L + \beta \gamma \sqrt{D^2 + (\gamma x_0 - \frac{L}{2})^2} - \beta \gamma \sqrt{D^2 + (\gamma x_0 + \frac{L}{2})^2}$$I am trying to determine expressions for ##\tilde{L}(x_0)## when ##x_0 \rightarrow -\infty## and ##x_0...
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